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(CNN) -- Roughly two-thirds of the people questioned in a recent poll on abortion supported parental and spousal notification but opposed a constitutional amendment to ban the practice altogether.

The CNN/USA Today/Gallup poll conducted November 11-13 found that 69 percent of the 1,006 adults questioned were in favor of requiring minors to get parental consent to have an abortion, while 28 percent opposed that step.

A New Hampshire law requiring parental notification comes before the Supreme Court this week as it hears the first major abortion cases in five years. (Full story)

In the poll, 64 percent said that wives should inform their husbands before getting an abortion, but 34 percent were against such a rule.

Despite the support for restrictions, 61 percent of those questioned were opposed to a constitutional amendment to ban abortion.

Thirty-seven percent were in favor of an amendment to ban abortions, except when the life of the mother was at stake.

More than three-fourths of the respondents believe that abortion should be legal in varying circumstances.

Thirty-nine percent of the respondents said that abortion should only be legal in a few circumstances, 26 percent believe it should be legal in all circumstances, and 16 percent favor legal abortion in most circumstances.

Another 16 percent said it should not be legal under any circumstances, the poll showed.

The poll had a margin of error of plus or minus 3 percentage points.

The debate over abortion rights has been in the spotlight recently, with the issue topping the Supreme Court's docket and confirmation hearings coming in January for President Bush's choice to fill Sandra Day O'Connor's seat on the high court.

Bush in October picked federal appeals judge Samuel Alito to replace O'Connor after the withdrawal of his initial nominee, White House Counsel Harriet Miers.

Abortion has already been the focus of public debate over the nomination, with abortion-rights activists opposed to Alito, and it is certain to become a key issue in the confirmation hearings.

The choice to replace O'Connor could be pivotal. She has been a key swing vote in the past and has, for example, voted to strike down abortion laws that failed to contain health exceptions.

Alito has told senators in private meetings that he has "great respect" for precedents, including the 1973 Roe v. Wade ruling. But he would not say whether he would continue to uphold that decision.

This week, the court will also hear arguments on whether the federal government can use racketeering laws to go after the organizers of protests outside abortion clinics.

O'Connor has said she will remain on the court until her successor is confirmed.